On an integral-type operator from the Bloch space to mixed norm spaces

2016 ◽  
Vol 273 ◽  
pp. 624-630
Author(s):  
Hao Li
Keyword(s):  
Bloch Space ◽  
Type Operator ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Spaces

scholarly journals On an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Type Operator ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Mixed Norm Spaces ◽  
Norm Space ◽  
Type Spaces

The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.

scholarly journals Embeddings of harmonic mixed norm spaces on smoothly bounded domains in ℝn

2019 ◽  
Vol 17 (1) ◽  
pp. 1260-1268
Author(s):  
Miloš Arsenović ◽  
Tanja Jovanović
Keyword(s):  
Unit Ball ◽  
Bounded Domain ◽  
Maximal Function ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Type Operator ◽  
Mixed Norm ◽  
Bounded Domains ◽  
Function Type ◽  
Mixed Norm Spaces

Abstract The main result of this paper is the embedding $$\begin{array}{} \displaystyle \mathcal{B}^{s,r}_\beta({\it\Omega})\hookrightarrow \mathcal{B}^{s_1,r_1}_{\beta+(n-1)\big(\frac 1s-\frac 1{s_1}\big)}({\it\Omega}), \end{array}$$ 0 < r ≤ r1 ≤ ∞, 0 < s ≤ s1 ≤ ∞, β > –1, of harmonic functions mixed norm spaces on a smoothly bounded domain Ω ⊂ ℝn. We also extend a result on boundedness, in mixed norm, of a maximal function-type operator from the case of the unit disc and the unit ball to general domains in ℝn.

scholarly journals On an integral-type operator from the Bloch space into the QK(p,q) space

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 331-339 ◽  
Author(s):  
Songxiao Li
Keyword(s):  
Positive Integer ◽  
Integral Operator ◽  
Bloch Space ◽  
Type Operator ◽  
Integral Type ◽  
Little Bloch Space

Let n be a positive integer, 1 ? H(D) and ? be an analytic self-map of D. The boundedness and compactness of the integral operator (Cn ?,1 f )(z) = ?z 0 f (n)(?(?))1(?)d? from the Bloch and little Bloch space into the spaces QK(p, q) and QK,0(p, q) are characterized.

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